Even though Time Warner said it wasn't interested in being acquired by Murdoch's 21st Century Fox, most investors believe that Murdoch and his team would continue their pursuit of the prize.

Investors drove up Time Warner stock 17% to $83.13 on Wednesday after Fox confirmed that it had made an $80-billion offer for Time Warner, which owns HBO, Warner Bros. studio, TNT, TBS, Cartoon Network and CNN.

Fox shares, meanwhile, declined 6% to $33. But the stock did not collapse -- a welcome sign for Murdoch and his family. The trading signaled that investors might be inclined to go along with Fox's acquisition plans.

Fox will probably sweeten its offer to try to make a deal happen, said veteran media analyst Michael Nathanson. Investors and other analysts agreed.

"We believe this transaction makes strategic and financial sense -- even at $100 a share," Marci Ryvicker, a senior media analyst with Wells Fargo Securities, wrote in a research note.

A $100-a-share offer would be 18% higher than Fox's initial $85-a-share proposal, which Time Warner formally rejected July 8.

Ryvicker said that $85 a share established a new "floor" for Time Warner stock, which she thinks could rise to $105 a share.

If Fox were to offer $100 a share, the deal would be valued at $91 billion.

People with knowledge of Fox's strategy say the company plans to be disciplined in its approach, and would not bid above a certain price. However, it is unknown what the highest price that Fox would be willing to pay.

The relatively low cost of borrowing money, and Time Warner's long-term campaign to shed assets to focus on TV and movies appears to have contributed to the timing of Fox's bid.

DiClemente noted that Time Warner's HBO is a particularly attractive asset, "well-positioned for a digital media future."

Some investors have encouraged Fox to add more cash into the deal. The rejected bid was a mix of cash and Fox non-voting shares.

Fox has two classes of stock, and Murdoch and his family control 39% of the voting shares. That gives the Murdoch family wide latitude over the company's operations and decision making, an arrangement that the Murdochs would like to continue in a bulked up Fox.

But Time Warner, in a statement, said there was "significant risk and uncertainty" to the value of Fox's non-voting shares, and thus, another reason to say no.

Now that its offer has been made public, Fox appears to be hoping that Time Warner will be pressured to take the Fox offer more seriously.

The two companies have many of the same investors; about 70% of Time Warner shareholders also own Fox shares.

Murdoch’s top lieutenant, Chase Carey, chief operating officer of Fox, met with Time Warner Chief Executive Jeff Bewkes in early June for lunch, shortly after Time Warner completed a spinoff of its Time Inc. magazine unit.

Carey told him that Fox wanted to buy Time Warner.

Two weeks later, Fox followed up with a formal letter. On Wednesday, Bewkes told Time Warner employees that its board rejected the offer last week.

“Jeff Bewkes came of age during the AOL acquisition -- and he is inherently skeptical about these combinations,” said Christopher Marangi, a portfolio manager at Mario Gabelli's Gamco Investors, which owns Fox and Time Warner shares.

“But Rupert has never been shy about growing his company," Marangi said.

To help make the deal more palatable, Fox has offered to sell CNN so lawmakers and regulators would not be concerned about the prospect of one company owning two of the three cable news channels.